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Lesson Plan

Trail Mix Servings: Trajectory of Understanding

teaches Common Core State Standards CCSS.Math.Content.6.NS.A.1
teaches Common Core State Standards CCSS.Math.Practice.MP3
teaches Common Core State Standards CCSS.Math.Practice.MP4
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Students will understand the meaning and unit of reference of the dividend, divisor, and quotient. The structure of the task requires students to interpret a visual model, and to choose one of two given possible solutions. The suggested public discussion of student work shows a trajectory of understanding from a basic interpretation of the given visual through a more sophisticated understanding of interpreting one model with two references: a measuring cup and a serving. It is important to discuss this trajectory publicly with students given the difficulty of understanding dividing with fractions and with interpreting a model that shows division. Students in Grade 6 likely have a range of understanding of division and of the model. Four pieces of work are shown, beginning with a response that shows a basic understanding resulting in a quotient that is not reasonable (less than one serving). The next response shows an understanding of one serving, but the quotient contradicts the original problem situation (one serving is ¾ cup, not 4/4 cup). The third response shows an understanding that the result is one serving plus an additional part of a serving, but uses an incorrect reference for the extra part. Finally, the fourth response shows correct understanding and interpretation of the model.
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